The real twin paradox.
in [Relativity]
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From: colp on 2 Dec 2007 16:16 On Dec 3, 4:08 am, Bryan Olson <fakeaddr...(a)nowhere.org> wrote: > colp wrote: > > papar wrote: > >> None of the twins can (realistically) see anything from the other twin > >> but the signals he receives. > > > These signals can be described as clock ticks. According to SR, while > > the twins are in inertial frames the ticks that are sent by the other > > twin will be sent at a slower rate than the ticks that are sent from > > the twin's local clock. > > > It doesn't matter how long it takes for the tick signals to get from > > one twin to another. All that matters is that the rate that the ticks > > are generated by the other twin is slower becuase of the time dilation > > while they are in inertial frames. > > In SR, a twin's observation of the other's clock ticking slowly > is based on "how long it takes for the tick signals to get from > one twin to another." Not according to delta t = gamma delta t_0 it isn't. > Twin A sees the ticks arrive, and figures > how long ago each B, traveling at c in A's frame. When the ticks actually arrive isn't imporant to the paradox. The paradox is based on the fact that according to SR the ticks of the other twin are generated more slowly that the local ticks on both legs. To solve the paradox a description of the other twin generating ticks more quickly that the local clock is required. > > > Every signal than is sent must be > > received by the other twin in the experiment. > > Sure. Early in twin A's voyage, the ticks from B arrive very > slowly, even slower than B's clock is running in A's frame. > Just after turnaround, A receives one of B's ticks per tick > of A's own clock, because the ticks were sent in the same > frame in which A now resides. Late in the journey, the ticks > from B arrive faster than one per tick of A's clock. There are two effects here: time dilation and signal transit time. The signal transit time does not affect the SR prediction that the number of ticks sent will be reduced because of time dilation. > > Twin A views B's time as dilated, in both directions, but > that's after compensating for the transit time of the clock ticks. That's according to SR, and assuming that viewing the time of the other twin involves the propagation of EM signals in the normal way. > > > The paradox isn't apparent when the events are viewed from a single > > inertial frame. Minkowski diagrams represent events according to such > > a frame. > > This "paradox" is only apparent if one misunderstands SR. What am I misunderstanding? According to SR the time dilation of B as seen by A means that fewer ticks are sent by B than are sent by A during the periods spent by A in inertial frames. The number of ticks sent must equal the number received, so there should be an explanation for how B sends more ticks than A from A's point of view when A in not an inertial frame. > > [...] > > > The importance of acceleration is that it is the only situation where > > a twin might be able to experience an effect which compensates for > > the time dilation of the other twin. > > What is important is the change in frames at turn-around. In > reality changing frames requires some acceleration period, but > we can model the turn-around as instantaneous, as long as we > account for the net difference between the two frames. You are avoiding the problem of acceleration when your model includes an instantaneous turnaround. > > Consider a tick arriving at twin A, at A's turn-around time. How > long ago did it leave twin B? That depends on which frame we use. > In A's outgoing frame, light moves at c relative to A's outgoing > frame, and the tick left fairly recently. In A's returning frame, > light moves at c relative A's returning frame, so the tick left > long ago. The result is that A finds B's age has jumped forward. When the tick was sent is not important in solving the paradox. All that is important is accounting for the missing ticks. > > When I was baffled by the twin's paradox (the real one in which > twins end up different ages), here's the explanation that helped > me get SR: > > http://www.bartleby.com/173/9.html
From: bz on 2 Dec 2007 16:22 "Sue..." <suzysewnshow(a)yahoo.com.au> wrote in news:082bfdf7-28b0-46c5-9d09-26cb2f790bf3(a)i12g2000prf.googlegroups.com: > On Dec 2, 1:48 pm, bz <bz+...(a)ch100-5.chem.lsu.edu> wrote: >> "Sue..." <suzysewns...(a)yahoo.com.au> wrote in >> news:6bad4ee2-091c-4c19-baa3- >> ba76f89af...(a)e10g2000prf.googlegroups.com: >> >> > On Nov 30, 7:29 pm, bz <bz+...(a)ch100-5.chem.lsu.edu> wrote: >> >> > [...] >> > BTW... There is a recent, well informed post on sci.physics.research >> > that discusses some of the causes of errors in the GPS. >> >> > I realise you would take the opposite view but it left me >> > no confidence that the 7us/day correction can be attributed >> > to predicted motional effects wrt earth. Even if a science >> > quality geostationary oscillator was avalible as we discussed >> > it might take a Ouji board to pull the signal out of the >> > system's phase noise. >> >> Put pencil to paper before you make such silly statements. > > My pencil isn't that sharp. > >> >> Due to the speed of light, a 7 us / day represents an error of ~ 2.099 >> km / day in apparent satellite location. > > OK thanks for the calc. Well... maybe it wouldn't take a Ouji board > with the geostationary control. > > >> >> The ACTUAL satellite location (it travels at about 3.47 km/s) would >> only be off by about 1 inch but it be saying it was 2 km away from its >> actual location. >> >> Somehow, I suspect that a 2 km per day error in satellite position [or >> a 7 us error in the time it reports] would be noticeable. >> >> > > I think it is all lumped into the pre-launch correction and servo'd > thereafter. BBBBut, according to sue or her relatives (relativity according to sue), the on board clock should run at the same rate it sees the ground based clock running. > >> >> > Where is Tom Roberts with his error bars when ya need him? ;-) >> >> > The Sagnac interferometer at Wettzell >> >http://www.wettzell.ifag.de/LKREISEL/G/LaserGyros.html >> >> A 2 km displacement of the earths crust would probably be noticable >> with instruments a LOT less sensitive that this. >> >> > is now integrated with GPS so might be a good source of >> > data to settle that sort of issue without need for a dedicated >> > SV or heaven-forbid you and I have to take your 100Khz crystal >> > calibrator up there ourselves and show 'em how it's done. ;-) >> >> I would love to make the trip. I'll buy the crystals, you rent the >> rocket from the russians, ok? They should give you a special price >> because you like their physics. > > 'Till DVM makes good on gambling debts this is all > I can afford: > > <<Incredible Adventures makes it possible for you to > break the sound barrier and more in a real military > jet fighter. >> > http://www.incredible-adventures.com/migs/ > > Ya think that will make it? gnaw, but you could get a real bang out of it. > >:o) ;} -- bz please pardon my infinite ignorance, the set-of-things-I-do-not-know is an infinite set. bz+spr(a)ch100-5.chem.lsu.edu remove ch100-5 to avoid spam trap
From: Bryan Olson on 2 Dec 2007 17:41 colp wrote: > On Dec 3, 4:08 am, Bryan Olson <fakeaddr...(a)nowhere.org> wrote: >> colp wrote: >>> papar wrote: >>>> None of the twins can (realistically) see anything from the other twin >>>> but the signals he receives. >>> These signals can be described as clock ticks. According to SR, while >>> the twins are in inertial frames the ticks that are sent by the other >>> twin will be sent at a slower rate than the ticks that are sent from >>> the twin's local clock. >>> It doesn't matter how long it takes for the tick signals to get from >>> one twin to another. All that matters is that the rate that the ticks >>> are generated by the other twin is slower becuase of the time dilation >>> while they are in inertial frames. >> In SR, a twin's observation of the other's clock ticking slowly >> is based on "how long it takes for the tick signals to get from >> one twin to another." > > Not according to delta t = gamma delta t_0 it isn't. Not it colp-theory maybe, but I wrote "in SR". SR derives gamma from the signal traveling at speed c in each frame. >> Twin A sees the ticks arrive, and figures >> how long ago each B, traveling at c in A's frame. > > When the ticks actually arrive isn't imporant to the paradox. Because if one gets it right, the paradox simply goes away. > The > paradox is based on the fact that according to SR the ticks of the > other twin are generated more slowly that the local ticks on both > legs. To solve the paradox a description of the other twin generating > ticks more quickly that the local clock is required. Try using SR. No paradox there. >>> Every signal than is sent must be >>> received by the other twin in the experiment. >> Sure. Early in twin A's voyage, the ticks from B arrive very >> slowly, even slower than B's clock is running in A's frame. >> Just after turnaround, A receives one of B's ticks per tick >> of A's own clock, because the ticks were sent in the same >> frame in which A now resides. Late in the journey, the ticks >> from B arrive faster than one per tick of A's clock. > > There are two effects here: time dilation and signal transit time. The > signal transit time does not affect the SR prediction that the number > of ticks sent will be reduced because of time dilation. Two effects? The principle of relativity has more, as of course colp would know by now were he not so devoted to his own ignorance. http://www.bartleby.com/173/9.html > According to SR the time dilation of B as seen by A means that fewer > ticks are sent by B than are sent by A during the periods spent by A > in inertial frames. The number of ticks sent must equal the number > received, so there should be an explanation for how B sends more ticks > than A from A's point of view when A in not an inertial frame. Yep, the one SR predicts, and explained to colp many times. >> Consider a tick arriving at twin A, at A's turn-around time. How >> long ago did it leave twin B? That depends on which frame we use. >> In A's outgoing frame, light moves at c relative to A's outgoing >> frame, and the tick left fairly recently. In A's returning frame, >> light moves at c relative A's returning frame, so the tick left >> long ago. The result is that A finds B's age has jumped forward. > > When the tick was sent is not important in solving the paradox. > All that is important is accounting for the missing ticks. Easy: there are no missing ticks in SR. Colp-theory may be different, but SR has this right. -- --Bryan
From: bz on 2 Dec 2007 17:16 "Sue..." <suzysewnshow(a)yahoo.com.au> wrote in news:6c37bff6-2a61-4b85-948b-57b3d24b834b(a)i12g2000prf.googlegroups.com: > On Dec 1, 3:14 pm, bz <bz+...(a)ch100-5.chem.lsu.edu> wrote: >> "Sue..." <suzysewns...(a)yahoo.com.au> wrote >> innews:873636c4-2a93-4f87-88a4-19394f1d85f3(a)e6g2000prf.googlegroups.com: >> >> > SR *does* address clocks that are moving toward each other. >> > "General results of the Theory" >> >> random citation by Sue, only relevance is that it mentions SR >> >> >http://www.bartleby.com/173/15.html >> >> [quote] > >> Sue says that ONLY light clocks obey Einstein-Lorentz time >> equation.http://en.wikipedia.org/wiki/Proper_time[which 'she' has cited >> recently as a source of wisdom] >> show the equations of SR and how they can be derived using GR. >> >> It also shows the so-called twin paradox, and how it can be worked. >> >> There is no hint that 'proper time' only applies to light clocks. >> In fact, such a suggestion would seem to be highly 'improper', to me. > > Are you offering argument that the semantic operator > should be acceptable in mathematics? So, you are anti semantic? Semantics IS a math. But, I was just trying to make an appropriated pun. > I think you know > that it isn't. > > When using *time* in an expression, it is meaningless > without a process. Read the NIST definition of *second*. I am well aware that modern science is based upon operational definitions. That does NOT mean surgery is required to understand that more than one kind of clock should show the rate predicted by E-LT when viewed from another iFoR. > http://physics.nist.gov/cuu/Units/second.html > > I won't even defend my statement in the > context you offer it because you failed to port relevant > context with your quotes. Perhaps too much port on your part? Try two points to starboard, on your next tack. > I think you know better. (I am not > sure Einstein did know better, at least in 1905) > In this Hyperphysics page approprate context IS > included: (pictures too) > > << A clock in a moving frame will be seen to be > running slow, or "dilated" according to the Lorentz > transformation. The time will always be shortest as > measured in its rest frame. The time measured in the > frame in which the clock is at rest is called the > "proper time". >> > http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/tdil.html All the calculations on that page seem to support my contention and refute yours. Where does it say 'these calculations only apply to a light clock'? > > Is it clear to you that the light-path is the > only element which can change to conform to > the equations? Light-path and light clock are different animals. Information is conveyed via light paths but the information can be from a balance clock, a quartz clock, an atomic clock, an hour glass, decaying radioactive particles or a light clock [but not a sundial, it is too heavy to be a light clock]. Atomic clocks are NOT light clocks although they use light from the atomic transition to tick off the time. Yet they appear to tick slower as they move faster. If your theory were right, a light clock oriented parallel to the direction of travel and one oriented perpendicular to the direction of travel, built into the same clock case, carried on a space ship, would each give the SAME time to someone riding on the ship but would report different times to someone 'at rest' with respect to the moving ship. This clearly is not going to happen. > Whether the clock moves away from the observer > or the observer moves away from the clock, > the same equations should work. Eh ? Yep. As long as they are in iFoRs. > That is not the case if we > allow a balance clock to respond to > an accelerating force. > (The force is balanced on the wheel) That, of course, requires leaving an iFoR and going from SR to GR (for easy math). Then, it does, IF the balance wheel is correctly built and the acceleration is constant. My watch keeps good time, no matter what direction gravity is pulling on it. > That is not the case for the Fizeau > light-clock moving in dielectric media. > (the dielectric provides a preferred frame of > reference) So, you really DO think that a clock oriented parallel to the direction of travel will keep different time than ones perpendicular to the direction of travel, AS SEEN BY someone riding with the clocks! I doubt that anyone except HW, KS, and A few others would agree with you on that idea. > That would not be the case if light > could move inertially. (many of Einstein's > contemporaties and perhaps Einstein too thought > that light did move inertially) [as far as I know] Einstein thought that the speed of light was independent of the motion of the source. [as far as I know] Einstein (and others) thought (and still think) that light carries 'inertia' or more properly 'momentum' in the form of energy and even responds to the force of gravity, but not as if it had 'mass equivalent to the energy' _and_ traveled as Newton would have predicted. > The speed of light would be violated) I think that is one too many ')' marks. Not sure where the opening '(' was supposed. And not sure how the speed of light can be violated. Should we call for a kit to investigate the violation? > Rather than play word games to *win* > an argument or nurture a popular myth you > can gain some insight to the paradox if > you'll ask what role the light path plays > with each scenario and each clock type. > > If a clock is supposed to slow whether > moving to or from the observer, only > the Fizeau light clock has the necessary > elements. An observer *receeding* with it > will see it as in-sync with a stayhome > clock and therefor indicating the > *proper-time* at home. NO! An observer *receeding* with it will see the stay-at-home clock slowed by doppler shift. It takes TIME for those pulses to travel from the stay-at-home clock to the moving clock. The two clocks will definitely NOT stay 'in-sync'. Not even clocks influenced by the dialectric of space can do as you just described. Your statement requires the moving clock to slow in proportion to the distance away from the stay at home clock AND the velocity. You would have light clocks carried to the moon by slow transport slowed by the trip, by about 1.283 seconds. That idea is so messed up I can't politely describe it. Not even A would make such a suggestion. > > You may recognise, a moving clock is not > even required to derive the equation: > http://www.eden.rutgers.edu/~mbarbato/Remote%20Sensing_files/page0003.htm > ...but a light path IS required. Right. No clock at all required, but the equations derived are in t and tau, which represent time, and unless I am mistaken, put NO restrictions upon how time is measured [with the notable exceptions of the pendulum clocks and sundials being excluded]. No claim is made that the any apparent discrepancy in clock readings is 'actual' UNLESS the clocks are brought back together. In such a case, the claim, consistently made, and as far as I know, verified by all experiments to date, is that the distance traveled through space-time is 'invariant', therefor a clock that accumulates more 'mileage' on the space-o-meter necessarily accumulates less 'mileage' on the time-o-meter. > What Einstein says about inertia in 1905 is not the same > in 1920 and neither may be totally on-the-mark. Your claims seem to miss the mark, entire. > > <<One may define a quantity which is divergence free > analogous to the energy-momentum density tensor > of special relativity, but it is gauge dependent: i.e., > it is not covariant under general coordinate transformations. > Consequently the fact that it is divergence free does not > yield a meaningful law of local energy conservation. > Thus one has, as Hilbert saw it, in such theories > `improper energy theorems.' >> > http://www.physics.ucla.edu/~cwp/articles/noether.asg/noether.html Interesting reading, but I have NOT read anywhere anything she appears to have said that would back up your claims. -- bz please pardon my infinite ignorance, the set-of-things-I-do-not-know is an infinite set. bz+spr(a)ch100-5.chem.lsu.edu remove ch100-5 to avoid spam trap
From: Sue... on 2 Dec 2007 19:42
On Dec 2, 4:22 pm, bz <bz+...(a)ch100-5.chem.lsu.edu> wrote: > "Sue..." <suzysewns...(a)yahoo.com.au> wrote innews:082bfdf7-28b0-46c5-9d09-26cb2f790bf3(a)i12g2000prf.googlegroups.com: > > > > > > > On Dec 2, 1:48 pm, bz <bz+...(a)ch100-5.chem.lsu.edu> wrote: > >> "Sue..." <suzysewns...(a)yahoo.com.au> wrote in > >> news:6bad4ee2-091c-4c19-baa3- > >> ba76f89af...(a)e10g2000prf.googlegroups.com: > > >> > On Nov 30, 7:29 pm, bz <bz+...(a)ch100-5.chem.lsu.edu> wrote: > > >> > [...] > >> > BTW... There is a recent, well informed post on sci.physics.research > >> > that discusses some of the causes of errors in the GPS. > > >> > I realise you would take the opposite view but it left me > >> > no confidence that the 7us/day correction can be attributed > >> > to predicted motional effects wrt earth. Even if a science > >> > quality geostationary oscillator was avalible as we discussed > >> > it might take a Ouji board to pull the signal out of the > >> > system's phase noise. > > >> Put pencil to paper before you make such silly statements. > > > My pencil isn't that sharp. > > >> Due to the speed of light, a 7 us / day represents an error of ~ 2.099 > >> km / day in apparent satellite location. > > > OK thanks for the calc. Well... maybe it wouldn't take a Ouji board > > with the geostationary control. > > >> The ACTUAL satellite location (it travels at about 3.47 km/s) would > >> only be off by about 1 inch but it be saying it was 2 km away from its > >> actual location. > > >> Somehow, I suspect that a 2 km per day error in satellite position [or > >> a 7 us error in the time it reports] would be noticeable. > > > I think it is all lumped into the pre-launch correction and servo'd > > thereafter. > > BBBBut, according to sue or her relatives (relativity according to sue), > the on board clock should run at the same rate it sees the ground based > clock running. My view is: Motion far from a planet will not affect an atomic clock. A nearby planet will slow an atomic clock. (Pound-Rebka-Snider) A nearby spinning planet *may* slow an atomic clock even more. (Neil Ashby, Cliff Will) Even tho the cesium clocks are not *designed* as Sagnac interferometers they can resond to the Sagnac effect. That complicates the issue even more. > > > > > > > > >> > Where is Tom Roberts with his error bars when ya need him? ;-) > > >> > The Sagnac interferometer at Wettzell > >> >http://www.wettzell.ifag.de/LKREISEL/G/LaserGyros.html > > >> A 2 km displacement of the earths crust would probably be noticable > >> with instruments a LOT less sensitive that this. > > >> > is now integrated with GPS so might be a good source of > >> > data to settle that sort of issue without need for a dedicated > >> > SV or heaven-forbid you and I have to take your 100Khz crystal > >> > calibrator up there ourselves and show 'em how it's done. ;-) > > >> I would love to make the trip. I'll buy the crystals, you rent the > >> rocket from the russians, ok? They should give you a special price > >> because you like their physics. > > > 'Till DVM makes good on gambling debts this is all > > I can afford: > > > <<Incredible Adventures makes it possible for you to > > break the sound barrier and more in a real military > > jet fighter. >> > >http://www.incredible-adventures.com/migs/ > > > Ya think that will make it? > > gnaw, but you could get a real bang out of it. This thing has adjustment screws on it. http://www.wettzell.ifag.de/LKREISEL/G/LaserGyros.html Ya just tighten 'em down 'till it matches your theory. That is what we need. >:-) Sue... > bz |